Details

sample333.0ms

Algorithm

intervals

Results

190.0ms	111×	body	1280	valid
58.0ms	20×	body	2560	valid
44.0ms	56×	body	640	valid
13.0ms	23×	body	320	valid
7.0ms	36×	body	80	valid
4.0ms	10×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize53.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
2.4b	(tan (+ x eps))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `tan-quot` `add-log-exp`
2×	`pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `add-cube-cbrt`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

18.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series661.0ms

Counts

2 → 6

Calls

2 calls:

137.0ms	(- (tan (+ x eps)) (tan x))
524.0ms	(tan (+ x eps))

simplify594.0ms

Counts

31 → 31

Iterations

Iter	Nodes
done	5000
3	1176
2	355
1	137
0	68

prune207.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan eps) (tan x)))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
0.2b	(* (tan eps) (tan x))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
7×	`tan-quot`
6×	`pow1`
4×	`distribute-lft-out` `associate-/l*`
3×	`associate-/r` `flip3--` `associate-r` `associate-l*` `flip--` `associate-/l/`
2×	`sub-neg` `diff-log` `associate-/r/` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

10.0ms	(- 1 (* (tan eps) (tan x)))
31.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
12.0ms	(* (tan eps) (tan x))
114.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

160.0ms	(- 1 (* (tan eps) (tan x)))
308.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
139.0ms	(* (tan eps) (tan x))
539.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify1.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	1976
1	426
0	174

prune675.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.9b

localize96.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin eps) (sin x)) (cos x))
0.2b	(* (sin eps) (sin x))
0.2b	(* (sin eps) (sin x))
3.5b	(- (/ (sin x) (* (cos x) (- 1 (/ (/ (* (sin eps) (sin x)) (cos x)) (cos eps))))) (/ (sin x) (cos x)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`times-frac`
3×	`associate-/r*` `prod-exp` `cbrt-unprod` `div-inv` `sin-mult`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `frac-sub` `flip--` `associate-/l*` `associate-/l/`

Counts

4 → 77

Calls

4 calls:

10.0ms	(/ (* (sin eps) (sin x)) (cos x))
9.0ms	(* (sin eps) (sin x))
15.0ms	(* (sin eps) (sin x))
87.0ms	(- (/ (sin x) (* (cos x) (- 1 (/ (/ (* (sin eps) (sin x)) (cos x)) (cos eps))))) (/ (sin x) (cos x)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (* (sin eps) (sin x)) (cos x))
57.0ms	(* (sin eps) (sin x))
60.0ms	(* (sin eps) (sin x))
331.0ms	(- (/ (sin x) (* (cos x) (- 1 (/ (/ (* (sin eps) (sin x)) (cos x)) (cos eps))))) (/ (sin x) (cos x)))

simplify1.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1582
1	347
0	143

prune794.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.8b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin eps) (sin x)) (cos x))
0.2b	(* (sin eps) (sin x))
0.2b	(* (sin eps) (/ (sin x) (cos x)))
3.5b	(- (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (/ (sin x) (cos x))) (cos eps))))) (/ (sin x) (cos x)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cbrt-cube` `associate-r` `add-exp-log` `add-cube-cbrt`
14×	`times-frac`
8×	`pow1`
6×	`associate-l` `add-log-exp`
4×	`prod-exp` `cbrt-unprod` `div-inv`
3×	`cbrt-undiv` `associate-/r*` `div-exp` `unswap-sqr`
2×	`pow-prod-down` `*-commutative` `sin-mult` `distribute-lft-out--` `difference-of-squares`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `associate-r/` `frac-sub` `flip--` `associate-/l` `associate-/l/`

Counts

4 → 90

Calls

4 calls:

21.0ms	(/ (* (sin eps) (sin x)) (cos x))
21.0ms	(* (sin eps) (sin x))
30.0ms	(* (sin eps) (/ (sin x) (cos x)))
78.0ms	(- (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (/ (sin x) (cos x))) (cos eps))))) (/ (sin x) (cos x)))

series694.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (* (sin eps) (sin x)) (cos x))
73.0ms	(* (sin eps) (sin x))
127.0ms	(* (sin eps) (/ (sin x) (cos x)))
347.0ms	(- (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (/ (sin x) (cos x))) (cos eps))))) (/ (sin x) (cos x)))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5002
2	2624
1	470
0	184

prune830.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.8b

regimes339.0ms

Accuracy

0% (0.4b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample10.5s

Algorithm

intervals

Results

6.0s	3324×	body	1280	valid
1.9s	1870×	body	640	valid
1.6s	637×	body	2560	valid
438.0ms	731×	body	320	valid
203.0ms	1103×	body	80	valid
111.0ms	335×	body	160	valid